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MOTION                                       87
84.   Unit Angle.  In the last equation 6=1 when S=T; therefore the angle which is subtended at the center of a circle by an arc equal to the radius is the unit of angle. This unit is called the radian.    Angles and angular displacements have no dimensions.    Why?
85.   Angular Velocity.  The conception of angular velocity is similar to that of linear velocity.    It is the time rate at which the axial plane sweeps over an angle.   When constant it is numerically equal to the angle swept over per second.   If we denote the angular velocity by ca its magnitude is defined by
-I-*-
Angular velocity is a vector quantity which is represented by a vector drawn along the axis of rotation. The vector points towards the observer when the rotation is counterclockwise, and away from the observer when it is clockwise. The angular velocity is said to be positive in the first case and negative in the second case. Angular velocity has the dimensions of the reciprocal of time.
The unit of angular velocity is the radian per
sec.
The relation between the linear and the angular velocities of a particle may be obtained from equations (VI) and (I).
"==~di
ds cos <t>
      r ""     Jt
(vii)